Add oil to a large skillet over medium-high heat. Season the salmon on both sides with salt and pepper. Once the oil is hot, slowly place the salmon filets, skin side down, onto the pan. Let it cook without moving it for about 5 minutes, until the bottom gets a nice crisp crust.
After 5 or 6 minutes, gently flip the filets over and cook for another 2 to 4 minutes, just until the salmon is fully cooked. Transfer salmon to plates and set aside.
In a food processor, add the basil leaves, parsley, garlic, and almonds. Process, and while the ingredients are mixing, pour in the olive oil through the top of the food processor. Season with salt and pepper and process. Taste, add more salt and pepper if needed, then spoon on top of the salmon and serve.
Notes
Searing the salmon: Sear the skin side down first. It's much easier to flip the salmon after it forms a crispy crust on that side. Trying to flip the fish when searing the exposed flesh side first could end up breaking the delicate filet.